I don't care about taxis that much. But I do have a degree in economics and actually wrote a thesis, in part, on technological lock-in and naturally occurring monopolies.
Most things don't become monopolies, so the burden of proof goes the other way. And there's nothing about self-driving taxis that makes them a monopoly. For the most part a natural technological lock-in has an insurmountable network effect, the canonical example is the design of the typewriter keyboard.
In all contexts what happens is an environment where your decision to use a product makes it more valuable for all other users. Like a fax machine. Or Facebook.
Taxis are literally the opposite of this. The more people using a taxi service the longer I have to wait for a cab. Yes, you will quickly point out that the bigger the service the more that service be available wherever I tend to go.
But those two forces are in direct contradiction to each other and as such the network effects of taxi services are weak at best.
Sure you can create a hypothetical world monopoly autonomous taxi company. I can always create another company, buy a dozen self-driving taxis, and post them outside giant sporting events or clubs at closing time with graphics on the side saying download this app to rent me, and someone will do it. There goes your monopoly.
The whole freaking point of monopolies is that they happen when the switching costs are extremely high or when the supply is constrained and someone corners it. Switching costs will always be zero, and there's absolutely no chance whatsoever that one single company will permanently be the only one that creates a working autonomous vehicle.
So as neither of those conditions apply, there's no obvious force towards a permanent monopoly. In fact the reason for the government created monopolies we do see is the fact that the market tends toward commoditization and a downward spiral in prices.
The market for taxi services is unusually competitive. That's why we got to where we are in the first place.